Heat Transfer Handbook part 107 ppsx

BOOKCOMP, Inc. — John Wiley & Sons / Page 1057 / 2nd Proofs / Heat Transfer Handbook / Bejan ROUGH SURFACES 1057 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1057], (29) Lines: 549 to 560 ——— 0.0pt PgVar ——— Normal Page PgEnds: T E X [1057], (29) on the basis of equal pumping power, it was shown that CHFs for the rough tubes were up to 80% higher than those for smooth tubes. Murphy and Truesdale (1972) have shown further that subcooled CHF tends to decrease by as much as 15 to 30% with increasing roughness height. In another study (Gomelauri and Magrakvelidze, 1978) with two-dimensional structured roughness, CHF is found to be dependent on the degree of subcooling. Swenson et al. (1962) and Watson et al. (1974) employed integral multistart helical ribs and found that at subcritical pressures, film boiling was inhibited and much higher heat fluxes could be sustained with lower mass fluxes in comparison with a smooth tube. Kitto and Wiener (1982) have reported as much as a threefold increase in CHF under nonuniform circumferential heating ribbed tubes. Three more recent studies (Celata et al., 1994; Kabata et al., 1996; Lan et al., 1997) have experimented with wire-coil inserts and found considerable enhancement in CHF. Celata et al. (1994) have reported up to 50% higher subcooled boiling CHF in comparison with that in a smooth tube for the same conditions. The subcooled water boiling data of Kabata et al. (1996) show as much as 90% CHF enhancement. Similarly, Lan et al. (1997) found two- to threefold increases in CHF in a R-113 system; they have also proposed a tentative correlation for predicting CHF under subcooled conditions. The use of helical ribbed tubes in high-pressure power boilers have long been considered in the literature (Bergles, 1998), and they have been shown to increase the heat transfer coefficient and CHF in once-through boiling of water (Swenson et al., 1962). Ribbed tubes also tend to suppress pseudo-film boiling (Ackerman, 1970) and increase the heat transfer coefficient in the post-CHF, dispersed-flow film boiling regime (Bergles, 1998). Commercial structured rough surfaces in the form of corrugated (or fluted, or convoluted) tubing have come to be employed extensively in refrigerant evaporators. Withers and Habdas (1974) have reported up to 100% increase in the heat transfer coefficient and up to 200% enhancement in CHF in bulk boiling of R-12 in helically corrugated tubes. In a more recent study on flow boiling of R-134a in a horizontal spirally fluted tube (MacBain et al., 1997), considerable enhancement in the heat transfer coefficient, which tends to increase with quality (a condition contrary to that in a smooth tube), has been reported. Artificial roughness in the form of longitudinal ribs or grooves has also been applied in gravity-driven, horizontal-tube, spray-film evaporators. However, although this type of surface might promote turbulence, it tends to impede film drainage (Bergles, 1998). Three-dimensional roughness, as obtained in knurled surfaces, for example, tends to promote turbulence as well as the liquid spreading over the surface. In this case, heat transfer coefficients have been found to increase as much as 100% (Cox et al., 1969). The contrasting recommendation of Newson (1978), based on the results for single-phase film or trickle coolers, is to employ longitudinal-rib-type roughness for horizontal-tube multiple-effect evaporators. 14.3.3 Condensing Film condensation of steam on vertical tubes with external pyramid-shaped, closely knurled artificial surface roughness was perhaps first investigated by Medwell and BOOKCOMP, Inc. — John Wiley & Sons / Page 1058 / 2nd Proofs / Heat Transfer Handbook / Bejan 1058 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1058], (30) Lines: 560 to 569 ——— 0.0pt PgVar ——— Normal Page PgEnds: T E X [1058], (30) Nicol (1965), and Nicol and Medwell (1966). With gravity-driven condensate drain- age, the mean heat transfer coefficient was found to increase significantly, with the roughest tube providing a twofold higher h than that in the reference smooth tube. Similarly, four- to fivefold higher condensing coefficients for R-11 have been reported by Carnavos (1980) or knurled tubes, although part of this enhancement may be due to an area increase. Thomas (1967) attached axial wires around the periphery of vertical smooth tubes, which facilitated better surface tension–driven condensate film drainage, to produce three- to fourfold enhancement in heat transfer. It was shown further that square-profiled wires were more effective than circular ones of the same roughness height (Thomas, 1968). These findings have been further corroborated by the analysis presented by Rifert and Leont’yev (1976), and the patent obtained by Kun and Ragi (1981) also describes closely spaced, attached-wire surface roughness on vertical tubes. Commercial corrugated or fluted tubes have been considered extensively for en- hancement of vapor space condensation, and their application was perhaps first advo- cated and shown to be beneficial by Withers and Young (1971). Subsequently, one of the most comprehensive investigations of steam condensation on vertical fluted tubes was performed by Newson and Hodgson (1973). Experimental data for 32 tubes with flute (or different helical corrugation) geometries were obtained, and the condensa- tion heat transfer coefficient was found to be enhanced by factors of 1.45 to 6.75 over that for smooth tubes. In steam condensation on horizontal helically corrugated tubes, Mehta and Raja Rao (1979) and Zimparov et al. (1991), among some others (Webb, 1994; Das et al., 2000), have reported about 1.1 to 1.4 enhancement factors (ratio of rough to smooth tube h’s). Typical enhancement in the Mehta and Raja Rao (1979) data is shown in Fig. 14.15. Similarly, Dreitser et al. (1988) have reported 1.8 to 2.65 times higher steam condensation heat transfer coefficients on horizontal tubes with transverse grooves or corrugations. Rough surfaces have been found to enhance in-tube forced-convective conden- sation as well. In an early study on the performance of horizontal-tube, multiple- effect desalination plants, Cox et al. (1970) could improve the overall heat transfer coefficients, with forced convection condensation inside and spray film evaporation outside, by using spirally indented and V-grooved tubes; although, it may be noted, a knurled surface tube was ineffective. Luu and Bergles (1979, 1981) have reported experimental data for condensation of R-113 in tubes with helical repeated rib in- ternal roughness and deep spirally fluted tubes. The average coefficients were found to increase by as much as 80% above smooth-tube values in the former case, and by 50%, on an envelope diameter basis, in the latter. Similarly, for R-22, Shinohara and Tobe (1985) observed a 59% increase in the condensation coefficients with a corrugated tube, and Chiang (1993) has reported a 10 to 20% increase with a heli- cally grooved tube. Wang (1987) has considered wire-coil inserts for stratified flow, in-tube condensation of R-12, to obtain 35 to 40% average enhancement. Wire-coil inserts (0.051 ≤ e/d ≤ 0.118, 0.512 ≤ p/d ≤ 1.024) have also been used in a more recent study (Akhavan-Behabadi et al., 2000) on condensation of R-22, and up to 100% enhancement in heat transfer coefficients is reported; a Nusselt number correlation, based on their own data set, has also been proposed. A method to produce BOOKCOMP, Inc. — John Wiley & Sons / Page 1059 / 2nd Proofs / Heat Transfer Handbook / Bejan EXTENDED SURFACES 1059 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1059], (31) Lines: 569 to 597 ——— 0.097pt PgVar ——— Normal Page PgEnds: T E X [1059], (31) Figure 14.15 Data for enhanced steam condensation heat transfer on a horizontal corrugated tube reported by Mehta and Raja Rao (1979). sand-grain-type random roughness by attaching metallic particles, which cover 50% of the surface area with an average roughness of e/d = 0.031, is described in a U.S. patent by Fenner and Ragi (1979). They have also shown that condensation increased by 300% for x>0.6 and by 140% for lower qualities in a refrigerant R-12 system. 14.4 EXTENDED SURFACES Extended or finned surfaces are perhaps the most widely used and researched of all enhancement techniques. Their applications cover a broad spectrum of heat exchange devices, which include finned tubes for shell-and-tube exchanges (Fig. 14.16), plate fins for compact heat exchanger (Fig. 14.17), and finned heat sinks for electronic cooling (Fig. 14.18), among others. Several monographs, reviews, and edited texts (e.g., Kern and Kraus, 1972; Zhukauskas, 1989; Shah et al., 1990; Bergles, 1990; Manglik and Kraus, 1996; Kakac¸ et al., 1999; Kraus et al., 2001) provide extended discussions on various aspects of fins, their design optimization, and applications. 14.4.1 Single-Phase Flow Enhanced heat transfer from finned surfaces by buoyancy-driven natural or free con- vection has been considered primarily for cooling of electrical and electronic de- vices and for hot-water baseboard room heaters. Of these, with new advancements in BOOKCOMP, Inc. — John Wiley & Sons / Page 1060 / 2nd Proofs / Heat Transfer Handbook / Bejan 1060 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1060], (32) Lines: 597 to 597 ——— 0.854pt PgVar ——— Normal Page PgEnds: T E X [1060], (32) Figure 14.16 Tubes with circumferential and strip fins on their outer surface for shell-and- tube heat exchangers. (Courtesy of Wieland-Werke AG.) Figure 14.17 Some enhanced fin geometries used in (a) plate fin and (b) tube plate fin compact heat exchangers. BOOKCOMP, Inc. — John Wiley & Sons / Page 1061 / 2nd Proofs / Heat Transfer Handbook / Bejan EXTENDED SURFACES 1061 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1061], (33) Lines: 597 to 605 ——— -1.643pt PgVar ——— Normal Page PgEnds: T E X [1061], (33) Figure 14.18 Typical finned heat sinks used for electronic cooling. (Courtesy of EG&G Wakefield Engineering.) building/room heating equipment, the use of baseboard heaters has declined consid- erably; in fact, this practice is close to being discontinued. For thermal management of microelectronic devices, on the other hand, much recent effort has been directed toward the development of high-performance extended-surface heat sinks, and it con- tinues to attract attention in the worldwide literature. A variety of fins are used, and some typical geometries are shown in Fig. 14.18. The design of these heat sinks en- tails optimization of the shape, size, and spacing of fin arrays, and their heat transfer characteristics have been covered in great detail in several reviews and monographs (Kraus, 1982; Nakayama and Bergles, 1990; Kraus and Bar-Cohen, 1995). In this context, one of the earliest studies on free convection from a pair of isothermal plates or fins was reported by Elenbaas (1942). It may also be noted that the use of extended surfaces for cooling electronic devices is not restricted to the natural convection heat transfer regime, but, in fact, the ever-increasing developments in high-performance microelectronics demand forced-convective heat transfer as well as other enhance- ment strategies (Bergles, 1986, 1990). In single-phase forced-convective applications, tubes with fins on the inner, outer, or both surfaces have long been used in double-pipe and shell-and-tube heat exchang- ers (Kern and Kraus, 1972; Fraas, 1989; Hewitt, 1992; Hewitt et al., 1993; Kraus et al., 2001, Kakac¸ and Liu, 2002). Some examples of finned tubes that are typically employed are shown in Figs. 14.16 and 14.19. Although experimental data for sev- eral different geometries and flow arrangements are reported in the literature (Webb, 1994; Bergles, 1998), few predictive correlations for the Nusselt number and friction factor have been devised. In recent times, theoretical studies based on computational BOOKCOMP, Inc. — John Wiley & Sons / Page 1062 / 2nd Proofs / Heat Transfer Handbook / Bejan 1062 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1062], (34) Lines: 605 to 631 ——— -0.2198pt PgVar ——— Normal Page * PgEnds: Eject [1062], (34) Figure 14.19 Examples of the variety in inner-finned tubes used in heat exchangers. (Cour- tesy of Noranda Metal Industries, Inc.) simulations of forced convection in finned tubes and annuli have also been reported in the literature. These analyses have addressed both laminar (Masliyah and Nandaku- mar, 1976; Prakash and Liu, 1985; Rustom and Soliman, 1988; Kettner et al., 1991; Shome and Jensen, 1996; and several others) and turbulent (Patankar et al., 1979; Said and Trupp, 1984; Edwards and Jensen, 1994; Liu and Jensen, 1999, 2001; and others) flows, where, in some cases, the modeling includes fins of finite thickness, helical or spiral fins, and a conjugate analysis–based fin effectiveness. Extended discussions of some of the computational modeling issues and their implications for the numerical results are given by Webb (1994), Edwards and Jensen (1994), Shome and Jensen (1996), and Liu and Jensen (2001). For internally finned tubes with straight or spiral fins and laminar flows, Watkinson et al. (1975) give the following hydraulic-diameter-based common expression for the isothermal Fanning friction factor and two different equations for the respective Nusselt numbers: f h = 16.4 Re h  d h d  1.4 (14.14) For straight fin tubes, Nu h = 1.08 × log Re h n 0.5  1 + 0.01Gr 1/3 h  Re 0.46 h · Pr 1/3  L d h  1/3  µ w µ b  0.14 (14.15) For spiral fin tubes, Nu h = 8.533 × log Re h 1 + 0.01Gr 1/3 h Re 0.26 h · Pr 1/3  t p  0.5  L d h  1/3  µ w µ b  0.14 (14.16) BOOKCOMP, Inc. — John Wiley & Sons / Page 1063 / 2nd Proofs / Heat Transfer Handbook / Bejan EXTENDED SURFACES 1063 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1063], (35) Lines: 631 to 660 ——— 1.43018pt PgVar ——— Normal Page * PgEnds: Eject [1063], (35) For f h and Nu h in turbulent flows in tubes with straight and spiral fins, Carnavos (1979a) has recommended the following: f h = 0.046Re −0.2 h  A f A fi  0.5 (sec α) 0.75 (14.17) Nu h = 0.023Re 0.8 h · Pr 0.4  A f A fi  0.1  A i A  0.5 (sec α) 3 (14.18) These correlations have been shown to describe the data for air, water, oil, and ethylene glycol (Watkinson et al., 1975; Carnavos, 1979a; Marner and Bergles, 1989). An attractive variation is to use segmented or interrupted longitudinal fins inside circular tubes, which are considered to promote enhanced heat transfer by periodi- cally disrupting and restarting the boundary layer on the fin surface and perturbing the bulk flow field in general. The experimental data for airflows in such tubes reported by Hilding and Coogan (1964) indicate thermal–hydraulic performance improvements in the laminar and transition flow regimes; very few benefits were seen in turbulent flows. Kelkar and Patankar (1990) have also considered segmented fins inside cir- cular tubes and have computationally simulated laminar forced convection in tubes with zero-thickness fin segments arrayed along the length of the tube in both an in-line and staggered arrangement. The in-line segmented fins, which had half the fin surface area of staggered or continuous fins, were found to perform better with 6% higher Nu and 22% lower f . Longitudinal fins and their modified varieties of the interrupted cut-and-twisted (Gunter and Shaw, 1942), perforated, and serrated types, as well as offset strip or lanced-type fins (see Fig. 14.16), are also commonly used in the annuli of double-pipe heat exchangers (Kern and Kraus, 1972; Webb, 1994; Bergles, 1998). Some design guidelines, data, and limited sets of predictive correlations are given by Kern and Kraus (1972), Guy (1983), Taborek (1997), and Kakac¸ and Liu (2002). Also, internally finned tubes can be “stacked” to provide multiple internal passages of the type shown in Fig. 14.19 with rather small hydraulic diameters (Soliman and Feingold, 1977; Carnavos, 1979b; Soliman, 1989). For crossflow over finned tube banks, a fairly large set of experimental data can be found in the Russian literature (Zhukauskas, 1989), and the recommended corre- lations for tubes with circular or helical fins are given below. It should be noted here that the Reynolds number is based on the maximum flow velocity in the tube bank given by U max = U ∞ × max  S T S T − D , S T /2  S 2 L + (S T /2) 2  1/2 − D  and Re = ρU max D µ (14.19) where S T and S L are the transverse and longitudinal pitch, respectively, of the tube array. Also, based on the work of Lokshin and Fomina (1978) and Yudin (1982), the friction loss is given in terms of the Euler number and the pressure drop is obtained from BOOKCOMP, Inc. — John Wiley & Sons / Page 1064 / 2nd Proofs / Heat Transfer Handbook / Bejan 1064 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1064], (36) Lines: 660 to 731 ——— 1.83615pt PgVar ——— Short Page * PgEnds: Eject [1064], (36) ∆p = Eu(ρV 2 ∞ N L )C z (14.20) where C z is a correction factor for tube bundles with N L < 5 rows of tubes in the flow direction, and is as follows: N L Aligned Staggered 1 2.25 1.45 2 1.6 1.25 3 1.2 1.1 4 1.05 1.05 ≥ 5 1.0 1.0 For in-line tubes with circular or helical fins, Eu = 0.068ε 0.5  S T − 1 S L − 1  −0.4 (14.21) for 10 3 ≤ Re ≤ 10 5 , 1.9 ≤ ε ≤ 16.3, 2.38 ≤ S T /D ≤ 3.13, and 1.2 ≤ S L /D ≤ 2.35. Nu = 0.303ε −0.375 · Re 0.625 · Pr 0.36  Pr Pr w  0.25 (14.22) for 5 × 10 3 ≤ Re ≤ 10 5 , 5 ≤ ε ≤ 12, 1.72 ≤ S T /D ≤ 3.0, 1.8 ≤ S L /D ≤ 4.0. For staggered tubes with circular or helical fins, Eu = C 1 · Re a · ε 0.5  S T D  −0.55  S L D  −0.5 (14.23) where C 1 =                      67.6,a=−0.7 for 10 2 ≤ Re < 10 3 , 1.5 ≤ ε ≤ 16, 1.13 ≤ S T /D ≤ 2.0, 1.06 ≤ S L /D ≤ 2.0 3.2,a=−0.25 for 10 3 ≤ Re < 10 5 , 1.9 ≤ ε ≤ 16, 1.6 ≤ S T /D ≤ 4.13, 1.2 ≤ S L /D ≤ 2.35 0.18,a= 0 for 10 5 ≤ Re < 1.4 × 10 6 , 1.9 ≤ ε ≤ 16, 1.6 ≤ S T /D ≤ 4.13, 1.2 ≤ S L /D ≤ 2.35 Nu = C 2 · Re a · Pr b  S T S L  0.2  p f D  0.18  h f D  −0.14  Pr Pr w  0.25 (14.24) where BOOKCOMP, Inc. — John Wiley & Sons / Page 1065 / 2nd Proofs / Heat Transfer Handbook / Bejan EXTENDED SURFACES 1065 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1065], (37) Lines: 731 to 787 ——— 4.60123pt PgVar ——— Short Page * PgEnds: Eject [1065], (37) C 2 =    0.192,a= 0.65,b= 0.36 for 10 2 ≤ Re ≤ 2 × 10 4 0.0507,a= 0.8,b= 0.4 for 2 ×10 4 ≤ Re ≤ 2 × 10 5 0.0081,a= 0.95,b= 0.4 for 2 ×10 5 ≤ Re ≤ 1.4 × 10 6 and the general range of the following fin and tube pitch parameters: 0.06 ≤ pf D ≤ 0.36, 0.07 ≤ h f D ≤ 0.715, 1.1 ≤ S T D ≤ 4.2, 1.03 ≤ S L D ≤ 2.5 In eqs. (14.22)–(14.24), the variables that describe the fin dimensions are ε ≡ finned surface extension ratio (i.e., ratio of total surface area and the bare tube surface area), p f ≡ fin pitch, and h f ≡ fin height. Plate-fin or tube-and-plate fin type of compact heat exchangers, where the finned surfaces provide a very large surface area density, are being used increasingly in many automotive, waste-heat recovery, refrigeration and air-conditioning, cryogenic, propulsion system, and other heat recuperation applications. A variety of finned sur- faces are used, typical among which include offset strip fins, louvered fins, perforated fins, and wavy fins, as illustrated in Fig. 14.17, which not only provide a surface-area enlargement but also increase the heat transfer coefficient by altering the flow field. Their development, thermal–hydraulic performance, and design methodologies, pri- marily for gas or air flows, have been the subject of several reviews and monographs (Manglik and Bergles, 1990; Kays and London, 1984; Shah et al., 1997; Webb, 1994; Smith, 1997; Shah et al., 1999; Hesselgreaves, 2001). The forced-convective gas flow in the interfin channels is rather complex, where the enhancement is generally due to flow separation, secondary flow, or periodic starting of the boundary layer, and relatively few generalized correlations or predictive methods are available. Of the many different compact heat exchanger enhanced plate-fin geometries, a more popular surface that finds wide use is the offset strip fin whose geometrical features are described in Fig. 14.20. Based on the experimental data for 18 different rectangular offset-strip-fin cores listed in Kays and London (1984) the following power law correlations for the Fanning friction factor f and Colburn factor j have been proposed (Manglik and Bergles, 1995): f h = 9.6243Re −0.7422 h α −0.1856 δ 0.3053 γ −0.2659  1 + 7.669 ×10 −8 Re 4.429 h α 0.920 δ 3.767 γ 0.236  0.1 (14.25) j h = 0.6522Re −0.5403 h α −0.1541 δ 0.1499 γ −0.0678  1 + 5.269 ×10 −5 Re 1.340 h α 0.504 δ 0.456 γ −1.055  0.1 (14.26) It should be noted that f h ,j h , and Re h in these equations are based on the hydraulic diameter that is defined as d h = 4shl 2(sl +hl +th) +ts (14.27) BOOKCOMP, Inc. — John Wiley & Sons / Page 1066 / 2nd Proofs / Heat Transfer Handbook / Bejan 1066 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1066], (38) Lines: 787 to 787 ——— * 15.854pt PgVar ——— Normal Page PgEnds: T E X [1066], (38) Figure 14.20 Geometrical features of rectangular offset strip plate fins. (From Manglik and Bergles, 1995.) Figure 14.21 Enhanced performance of sinusoidal wavy plate fin channels in periodically developed laminar flows as measured by the area goodness factor. (From Metwally and Man- glik, 2000.) . hot-water baseboard room heaters. Of these, with new advancements in BOOKCOMP, Inc. — John Wiley & Sons / Page 1060 / 2nd Proofs / Heat Transfer Handbook / Bejan 1060 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1060],. Medwell and BOOKCOMP, Inc. — John Wiley & Sons / Page 1058 / 2nd Proofs / Heat Transfer Handbook / Bejan 1058 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1058],. computational BOOKCOMP, Inc. — John Wiley & Sons / Page 1062 / 2nd Proofs / Heat Transfer Handbook / Bejan 1062 HEAT TRANSFER ENHANCEMENT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 [1062],